Corrector results for space-time homogenization of nonlinear diffusion

TL;DR

This paper establishes corrector results for space-time homogenization of nonlinear diffusion equations with oscillating coefficients, using unfolding methods and strong two-scale convergence, without smoothness assumptions.

Contribution

It provides the first corrector results for nonlinear diffusion in space-time homogenization without requiring smooth coefficients.

Findings

Strong convergence of solutions with correctors for gradients

Strong convergence of diffusion fluxes

Strong convergence of time derivatives

Abstract

The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of solutions with corrector terms) for gradients, diffusion fluxes and time-derivatives without assumptions for smoothness of coefficients. Proofs of the main results are based on the space-time version of the unfolding method, which is deeply concerned with the strong two-scale convergence theory.